Lesson 14: Practice Problems

Problem 1 From Unit 1 Lesson 9

Use the diagram to find the measure of each angle.

Line EC is intersected at point B by line AD. Angle CBD is 45 degrees.

$m ∠ A B C$
$m ∠ E B D$
$m ∠ A B E$

Problem 2

Lines $k$ and $ℓ$ are parallel, and the measure of angle $A B C$ is 19 degrees.

Points F, C, and D lie on line k, where point F is to the left of point C and point D is to the right of point C. Points A and B lie on line l, where point B is to the right of point A. Lines k and l are parallel, where line k is above line l, and both lines slant upward and to the right. A third line, labeled m, intersects lines k and l at point C and point B and has a point labeled E located to the left of point C.

Explain why the measure of angle $E C F$ is 19 degrees. If you get stuck, consider translating line $ℓ$ by moving $B$ to $C$ .
What is the measure of angle $B C D$ ? Explain.

Problem 3

The diagram shows three lines with some marked angle measures.

Find the missing angle measures marked with question marks.

Two lines intersected by another line. An angle of 70 deg is shown in one intersection and an angle in the same position in the other intersection is 53 deg

Problem 4

Lines $s$ and $t$ are parallel. Find the value of $x$ .

Two parallel lines s and t cut by a transversal at angle x on line s. A 4th line intersects t at the transversal and forms a 90 deg angle and intersects s at a 40 deg angle.

Problem 5

The two figures are scaled copies of each other.

Figure 1 has points ACD. Larger figure 2 has points PQRS. Corresponding Points are A and P, C and R, D and S.

What is the scale factor that takes Figure 1 to Figure 2?
What is the scale factor that takes Figure 2 to Figure 1?